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X₂₄₁₄¶

GIBERT-SIMSON TRANSFORM OF X₁₂₉₂

X₂₄₁₄ = trilinear pole of line X₁₂₀ X₅₁₈ (the Simson line of X₁₂₉₂)

X₂₄₁₄ (GIBERT-SIMSON TRANSFORM OF X₁₂₉₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2414 = GIBERT-SIMSON TRANSFORM OF X_1292."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02414(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2414 = GIBERT-SIMSON TRANSFORM OF X_1292 on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_277 = eval_trilinear_point(model, A, B, C, '(((sec(A/2))**(2))/(- (cos(A/2))**(4) + (cos(B/2))**(4) + (cos(C/2))**(4)))', ID="X_277", classes=["center"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center"])
            X_1292 = eval_trilinear_point(model, A, B, C, '1/((b - c)*(a**(2) + b**(2) + c**(2) - 2*a*b - 2*a*c))', ID="X_1292", classes=["center"])
            central_line(model, X_2, X_277, 2, 277)
            central_line(model, X_100, X_1292, 100, 1292)
            X_2414 = intersect_lines(model, X_2, X_277, X_100, X_1292, ID="X_2414", classes=["selected", "target"])
            return promote_point_to_top(model, X_2414)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_2414 on the given reference triangle."""
            model = create_model('X_2414 = GIBERT-SIMSON TRANSFORM OF X_1292')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02414(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-02414.json"))
            write_center_svg(
                model_acute,
                here / "x-02414.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2414¶

X₂₄₁₄¶